In △abc, ab=8, bc=10, and ac=12. let m, n, and k be the midpoints of the sides of △abc. find length of each side of △mnk.

The side lengths are 4, 5, and 6.

Step-by-step explanation:

Each midsegment is half the length of the parallel side, so the side lengths of ΔMNK are 4, 5, and 6.

It isn't clear which point is the midpoint of what segment. If it is true that ...

M is the midpoint of ABN is the midpoint of BCK is the midpoint of AC

then ...

MN = AC/2 = 6NK = AB/2 = 4KM = BC/2 = 5

1.   an exact solution requires a radical solution - no decimal approximation.2. (a)4x^3 = 756x^3 = 756/4 = 189x =   cube root of 189 =   5.74   to nearest hundredth answer(b)   189 = 3*3*3*7   so we can write the cube root of 189 as 3∛7 answerchecking (a) 4*(5.74^3 =   756.48   which is very close(b)   4* ((3∛3)^3   = 4*189   = 756   - spot on! 3. i would use solution b because the original question asked for an exact solution.